Figure 1a shows the crystal structure of the new FeSe-based superconductor: (Li\(_{1-x}\) Fe\(_x\) )OHFe\(_{1-y}\) Se[1]}, [2]}. It consists of FeSe layers sandwiched in between the (LiFe)OH layers along the c direction. The in-plane lattice constant a or b is 3.78 Å which is close to that (3.76 Å) in the bulk FeSe superconductor (T\(_c\)\(\sim \)  8.5 K)[3]}, but the distance of the two adjacent FeSe layers in (Li\(_{1-x}\) Fe\(_x\) )OHFe\(_{1-y}\) Se (9.32 Å) is much larger than that in bulk FeSe (5.5 Å)[3]}. This indicates a weak interaction between the two adjacent FeSe layers in (Li\(_{1-x}\) Fe\(_x\) )OHFe\(_{1-y}\) Se and its enhanced two-dimensional nature of the electronic structure compared with bulk FeSe. In comparison, the single-layer FeSe/SrTiO\(_3\)  film consists of a strictly two-dimensional Se-Fe-Se layer on the top of the SrTiO\(_3\)  substrate; the thickness of the FeSe layer is 5.5 \(Å\)  (Fig. 1b)[5]}. In comparison, the distance between the two adjacent FeSe layers in the A\(_x\) Fe\(_{2-y}\) Se\(_2\)  is 7.02 \(Å\) , however, there is an in-plane displacement between the two adjacent FeSe layers (Fig. 1c)[6]}. The latest success of growing high-quality large-sized (Li\(_{1-x}\) Fe\(_x\) )OHFe\(_{1-y}\) Se single crystals[2]} makes it possible to carry out ARPES measurements on the new superconductors. The sample we have measured in this paper has a composition of Li\(_{0.84}\) Fe\(_{0.16}\) OHFe\(_{0.98}\) Se (abbreviated as FeSe11111 hereafter) [2]} with a superconducting transition temperature T\(_c\)\(\sim \) 41 K (Fig. 3d).
